Question : Ram and Hari can cut 12 kg of nuts in 2 days. After five days, Hari left the job. Ram took 8 more days to cut the rest of the nuts. If a total of 58 kg of nuts were cut, the time taken by Hari to cut 10 kg of nuts is:
Option 1: 1 day
Option 2: 2 days
Option 3: 3 days
Option 4: 4 days
Correct Answer: 4 days
Solution :
Ram and Hari can cut 12 kg of nuts in 2 days.
The combined rate of cutting nuts = $\frac{12}{2} $ = 6 kg/day
They worked together for 5 days ⇒ Total nuts cut = (5 × 6) = 30 kg.
After that, Hari left and Ram cut the rest of the nuts alone.
The total weight of the nuts was 58 kg.
Remaining nuts = (58 – 30) = 28 kg.
It took Ram 8 more days to cut the rest of the nuts.
The rate of cutting nuts = $\frac{28 }{8 }$ = 3.5 kg/day
Since Ram and Hari's combined rate is 6 kg/day and Ram's rate is 3.5 kg/day, Hari's rate must be = (6 – 3.5) = 2.5 kg/day.
The time taken by Hari to cut 10 kg of nuts = $\frac{10 }{2.5 }$ = 4 days
Hence, the correct answer is 4 days.
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